Question

A three-year interest rate swap has a level notional amount of 300,000. Each settlement period is one year and the variable rate is the one-year spot interest rate at the beginning of the settlement period. One year has elapsed and the one-year spot interest rate at the start of year 2 is 4.45%.

Time to Maturity 1 2 3 4 5
Price of zero coupon bond with Maturity value 1 0.97 0.93 0.88 0.82 0.75
Calculate the net swap payment by the payer at the end of the second year.
A. −400
B. −300
C. −200
D. −100
E. 0
Hint : Find the swap rate R using the table and then use R and the one-year spot rate at the start of year 2 to find the net swap payment at the end of year 2.

Answer 1

A. -400

Explanation:

We solve for the swap rate

R = (1-p3)/(p1+p2+p3)

R = 1-0.88/0.97+0.93+0.88

= 0.12/2.78

= 0.04317

Remember 4.45% is the one year spot rate for the second option

Net swap

= 300000*0.04317-300000*0.0445

= 12951-13350

= -399

This is approximately -400

So the net swap payment at the end of the second year is option a, -400